Electrostatic Mechanism of Emission Enhancement in Hybrid Metal-semiconductor Light-emitting Heterostructures Page: 45
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P()(z) = i(sic ei qz,j(z-Zj) + +Be-i z,i(z-z))
For I-OP modes, the z-component of the wavevector is imaginary, meaning that the
solutions for the polarization take the form of a linear superposition of an exponential
growth and decay term. If we substitute iqz,j for q,j in Eq. 4.3.12 we can see that for the
region j=O which runs from - to 0, o must be zero such that P (-oo) = 0. Similarly, B10
= 0 so that P (oo) = 0.
For the remaining coefficients, we can relate the coefficients A and B of layer j to
those of layer j+1 by using the electrostatic boundary conditions for the polarization at
the zj interface:
x-1(W) pc (z) = X-1(W) pfl+l) (z)
X)z,j() Xz,j+(1() z=zj
The application of the BCs results in the following set of matrix relations for the
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Llopis, Antonio. Electrostatic Mechanism of Emission Enhancement in Hybrid Metal-semiconductor Light-emitting Heterostructures, dissertation, May 2012; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc115113/m1/55/: accessed October 20, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .